On Solving Linguistic Bi-Level Programming Problem Using Dynamic Programming

In this work, a linguistic bi-level programming problem has been developed where the functional relationship linking decision variables and the objective functions of the leader and the follower are not utterly well known to us. Because of the uncertainty in practical life decision-making situation...

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Bibliographic Details
Published in:International journal of fuzzy system applications Vol. 10; no. 1; pp. 43 - 63
Main Author: Singh, Vishnu Pratap
Format: Journal Article
Language:English
Published: Hershey IGI Global 01.01.2021
Subjects:
Decision making
Dynamic programming
Functionals
Fuzzy logic
Linguistics
India
ISSN:2156-177X, 2156-1761
Online Access:Get full text
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Summary:In this work, a linguistic bi-level programming problem has been developed where the functional relationship linking decision variables and the objective functions of the leader and the follower are not utterly well known to us. Because of the uncertainty in practical life decision-making situation most of the time, it is inconvenient to find the veracious relationship between the objective functions of leader, follower, and the decision variables. It is expected that the source of information which gives some command about the objective functions of leader and follower is composed by a block of fuzzy if-then rules. In order to analyze the model, a dynamic programming approach with a suitable fuzzy reasoning scheme is applied to calculate the deterministic functional relationship linking the decision variables and the objective functions of the leader as well as the follower. Thus, a bi-level programming problem is constructed from the actual fuzzy rule-based to the conventional bi-level programming problem. A numerical example has been solved to signify the computational procedure.
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ISSN:2156-177X
2156-1761
DOI:10.4018/IJFSA.2021010103